Solve (1/x+2/x^2)*x^4/12=

$$( \frac { 1 } { x } + \frac { 2 } { x ^ { 2 } } ) \cdot \frac { x ^ { 4 } } { 12 } =$$

Evaluate

$$\frac{\left(x+2\right)x^{2}}{12}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{1}{x} times \frac{x}{x}.

$$\left(\frac{x}{x^{2}}+\frac{2}{x^{2}}\right)\times \frac{x^{4}}{12}$$

Since \frac{x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x+2}{x^{2}}\times \frac{x^{4}}{12}$$

Multiply \frac{x+2}{x^{2}} times \frac{x^{4}}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)x^{4}}{x^{2}\times 12}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{\left(x+2\right)x^{2}}{12}$$

Use the distributive property to multiply x+2 by x^{2}.

$$\frac{x^{3}+2x^{2}}{12}$$

Expand

$$\frac{x^{3}}{12}+\frac{x^{2}}{6}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{1}{x} times \frac{x}{x}.

$$\left(\frac{x}{x^{2}}+\frac{2}{x^{2}}\right)\times \frac{x^{4}}{12}$$

Since \frac{x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x+2}{x^{2}}\times \frac{x^{4}}{12}$$

Multiply \frac{x+2}{x^{2}} times \frac{x^{4}}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)x^{4}}{x^{2}\times 12}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{\left(x+2\right)x^{2}}{12}$$

Use the distributive property to multiply x+2 by x^{2}.

$$\frac{x^{3}+2x^{2}}{12}$$